Fig. REF  shows J-factors of a few
selected ultrafaint dSphs that are found to have relatively large
J-factor. Here \(\theta =0.5^\circ \)  and \(V_{50}=\) 10.5 km s\(^{-1}\)  (left)
and 18 km s\(^{-1}\)  (middle) are adopted. As a comparison, the results
by log-uniform priors for both \(\rho _s\)  and \(r_s\)  with abrupt cut
according to cosmological argument (GS15
cut) [1]} is shown for comparison (right).
Shaded band shows 95% credible intervals, which are determined by the
posterior distributions of the J factor for a given value of
\(\epsilon _\phi \)  and \(\alpha _y\) . \(\epsilon _\phi \rightarrow \infty \)  limit
corresponds to the results without the Sommerfeld enhancement that are
consistent with those in Ref. [2]}. It is seen that
the median and credible region change in different values of \(V_{50}\) 
for a given \(\epsilon _\phi \) . It is found that they trace the value at
\(\epsilon _\phi \rightarrow \infty \)  limit; if the J-factor of a dSph for a
given \(V_{50}\)  in this limit is larger compared to another, then the
J-factor with finite \(\epsilon _\phi \)  is also larger. I.e., the
differences of J-factor are nearly independent of \(\epsilon _\phi \) .
